Question: The sum of two angles is $86^\circ$. Angle 2 is $114^\circ$ smaller than $3$ times angle 1. What are the measures of the two angles in degrees?
Answer: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 86}$ ${y = 3x-114}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${3x-114}$ for $y$ in the first equation. ${x + }{(3x-114)}{= 86}$ Simplify and solve for $x$ $ x+3x - 114 = 86 $ $ 4x-114 = 86 $ $ 4x = 200 $ $ x = \dfrac{200}{4} $ ${x = 50}$ Now that you know ${x = 50}$ , plug it back into $ {y = 3x-114}$ to find $y$ ${y = 3}{(50)}{ - 114}$ $y = 150 - 114$ ${y = 36}$ You can also plug ${x = 50}$ into $ {x+y = 86}$ and get the same answer for $y$ ${(50)}{ + y = 86}$ ${y = 36}$ The measure of angle 1 is $50^\circ$ and the measure of angle 2 is $36^\circ$.